What do these numbers mean?
Can you be mislead by statistics? The word "statistics" actually has
several meanings. It can refer to single facts such as the number of
people who like milk or the percentage of cats that is white. Statistics
are used to describe groups of numbers. The methods and techniques used
to collect, analyze and present a set of numbers are also called
statistics...you may have heard people call this "number crunching." In
research, statistics may be used to determine if a new drug or treatment
is useful. In business, statistics may be used to make new products or
services or to chart trends in public opinion.

Let's take a closer look at "numbers" to see how they are collected,
analyzed and displayed. If you know more about statistics, you should be
able to make better decisions about what and whom to believe.

Number
Crunching?

But first, let's get two things straight:

You do not have to be a math expert to understand the
basic concepts of statistics. A basic knowledge of math and a lot of
common sense will be fine.

It's about the word "data." The word "data" is plural. You should say
and write, "The data are ..." Do NOT say, "The
data is..." If you are talking about just one number, the word is
"datum."

Numbers

Data that
are actually collected are sometimes called "raw data." These are the
numbers that have been measured and recorded. Suppose we wanted to find
out if playing background music improves the running speed of rats in a
maze. In the experiment, 11 rats (rat #1 - rat #11) would run while
listening to music and 11 rats (rat #12 - rat #22) would run without
listening to music. We would measure the time it takes each rat to run
through the maze. The time (in seconds) for each rat to complete the maze
is recorded.

The Median

The median is another way to describe a set of numbers. The median is the
score that is exactly midway in the set of numbers. The easiest way to
find the median is to rank the numbers in order. If we rank the
scores from the music group in the rat maze data, it would look like:

11.1, 11.4, 18.2, 18.3, 18.8, 22.8, 26.3, 28.5, 29.7, 30.9, 33.3

Therefore, the median (the midway score) is 22.8 because there
are five scores higher than 22.8 (26.3, 28.5, 29.7, 30.9, 33.3) and five
scores lower than 22.8 (11.4, 12.1, 18.2, 18.3, 18.8).

If you had an even number of scores in your data set (for example, the
maze running times of 10 rats rather than 11 rats), the median would be
the midway point between the two middle numbers. For example, in the set
of numbers: 1, 2, 4, 6, 17, 20; the median is:

4 + 6=52

When you have an odd number of scores, you don't even have to know how to
add and divide to find the median. All you have to do is rank the numbers
from low to high and find the middle number.

Mode

The mode is a third way to describe a set of numbers. The mode is very
easy to find; it is the number that occurs most often. For example in
the set of numbers:

1, 4, 4, 4, 4, 4, 6, 6, 10, 11, 13,
15

the mode is 4 because it occurs the most times. The mode
does not provide very much information about a whole set of numbers. It
only tells what score occurs most frequently.

It is important to know
the average of a
group of numbers, but there is still more information to be squeezed out
of the raw data. For example, it is important to know how similar a
particular number is to the other numbers in the group. In other words,
the amount of variation in the data can be determined. The two most common
ways to describe variation are the range and the standard deviation.

The Range

The range is the difference between the highest value and the lowest
value in a sample. For example, in the set of numbers:
2, 2, 2, 7, 8, 9, 10, 11, 11, 15, 20, the range is:

20 - 2 = 18

Sometimes statisticians include the highest and lowest scores in
the range. In this case, you must add "1" to the calculation. In other
words:

20 - 2 + 1 = 19

The range is very easy to calculate, but it really does not give you very
much information because it ignores most of the data. The range is only
concerned with the highest and the lowest values.

The Standard Deviation

The standard deviation is a very common method used in science to describe
the variability in a set of numbers. It examines the spread (variability)
of each data point around the mean. The standard deviation increases with
an increase in the variability of the data. If every score in the data
set are the same, then the standard deviation will equal zero.